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For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the two-party t-message public-coin communication complexity of f with worst case error e. We show that for any relation f and positive integer k: R^{(t), pub}_{1 - 2^{-Omega(k/t^2)}}(f^k) = Omega(k/t (R^{(t), pub}_{1/3}(f) - O(t^2))) . In particular, it implies a strong direct product theorem for the two-party constant-message public-coin randomized communicati"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.1666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-01-08T23:31:01Z","cross_cats_sorted":[],"title_canon_sha256":"7b0d937950eeb68636fee2b5427b03dea903da95eecbcb51a7db6c5e273a1b90","abstract_canon_sha256":"56cb12cc34ed5870ac5bccba88a1f9a078a7cd6785c2ab01cfc26fcaa0aac2e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:02.862370Z","signature_b64":"AKX0g2Mt1cp3UEnydVIAvteSx0lIPsGbVkyHRg27cdlVaJ8OgNxhO3JaBSNhiV6fJWYsDZvhnSMl9p9RsRuMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccdbb56ab22b307590eed7b78f346353813cfc828109329d7d8cff3911af4ab5","last_reissued_at":"2026-05-18T04:05:02.861817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:02.861817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A direct product theorem for bounded-round public-coin randomized communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Attila Pereszlenyi, Penghui Yao, Rahul Jain","submitted_at":"2012-01-08T23:31:01Z","abstract_excerpt":"In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. 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